Representation Theorems for Analytic Machines and Computability of Analytic Functions

We present results concerning analytic machines, a model of real computation introduced by Hotz which extends the well-known Blum, Shub and Smale machines (BSS machines) by infinite converging computations. The well-known representation theorem for BSS machines elucidates the structure of the functions computable in the BSS model: the domain of such a function partitions into countably many semi-algebraic sets, and on each of those sets the function is a polynomial resp. rational function. In this paper, we study whether the representation theorem can, in the univariate case, be extended to analytic machines, i.e. whether functions computable by analytic machines can be represented by power series in some part of their domain. We show that this question can be answered in the negative over the real numbers but positive under certain restrictions for functions over the complex numbers. We then use the machine model to define computability of univariate complex analytic (i.e. holomorphic) functions and examine in particular the class of analytic functions which have analytically computable power series expansions. We show that this class is closed under the basic analytic operations composition, local inversion and analytic continuation.     

Robotic Assembly Processes as a Driver in Architectural Design

Over the last couple of years industrial robots have increasingly gained the interest of architects and designers. Robotics in architecture and construction has mainly been looked at from an engineering perspective during the latter half of the twentieth century, with the main purpose of automating the building process. Today the focus has turned towards realizing non-standardized designs and developing custom fabrication processes. However, the specific characteristics of the robot, which distinguish it from common computer numerically controlled machines, are often overlooked. Industrial robots are universal fabrication machines that lend themselves especially well to assembly tasks. Applied to architecture this resolves to the ability to control and manipulate the building process. As such, applying industrial robots emphasizes construction as an integral part of architectural design. Moreover, designing and manipulating robotic assembly processes can become a driver in architectural design. The potential of such an approach is discussed on the basis of several design experiments that illustrate that by applying such methods, form is not derived from computation or geometry, but from a physical process.     

Purkinje Images: Conveying Different Content for Different Luminance Adaptations in a Single Image

Providing multiple meanings in a single piece of art has always been intriguing to both artists and observers. We present Purkinje images, which have different interpretations depending on the luminance adaptation of the observer. Finding such images is an optimization that minimizes the sum of the distance to one reference image in photopic conditions and the distance to another reference image in scotopic conditions. To model the shift of image perception between day and night vision, we decompose the input images into a Laplacian pyramid. Distances under different observation conditions in this representation are independent between pyramid levels and pixel positions and become matrix multiplications. The optimal pixel colour can be found by inverting a small, per‐pixel linear system in real time on a GPU. Finally, two user studies analyze our results in terms of the recognition performance and fidelity with respect to the reference images.     

Decoupled Opacity Optimization for Points,Lines and Surfaces

Displaying geometry inflow visualization is often accompanied by occlusion problems, making it difficult to perceive information that is relevant in the respective application. In a recent technique, named opacity optimization, the balance of occlusion avoidance and the selection of meaningful geometry was recognized to be a view‐dependent, global optimization problem. The method solves a bounded‐variable least‐squares problem, which minimizes energy terms for the reduction of occlusion, background clutter, adding smoothness and regularization. The original technique operates on an object‐space discretization and was shown for line and surface geometry. Recently, it has been extended to volumes, where it was solved locally per ray by dropping the smoothness energy term and replacing it by pre‐filtering the importance measure. In this paper, we pick up the idea of splitting the opacity optimization problem into two smaller problems. The first problem is a minimization with analytic solution, and the second problem is a smoothing of the obtained minimizer in object‐space. Thereby, the minimization problem can be solved locally per pixel, making it possible to combine all geometry types (points, lines and surfaces) consistently in a single optimization framework. We call this decoupled opacity optimization and apply it to a number of steady 3D vector fields.     

Intangible Bonds: Cultural Ecosystem Services and Landscape Practices

This article sheds light on the complex interaction between humans and the natural world, as well as the significance of Cultural Ecosystem Services (CES) in interpreting this bond. CES refers to the non-material and immaterial benefits that nature gives to human society, including nature-based tourism, landscape aesthetics, sense of place, cultural heritage, and spiritual inspiration. However, the rapid social shifts have influenced both human behaviors and the human-nature relationships, while reshaping the supply–demand relationships between CES and people. For landscape practitioners, it is necessary to use innovative approaches to comprehend and appreciate the complex cultural links between the natural ecosystem and our cultural attachments, and build a more sustainable interaction via landscape practices. The authors claim that CES can act as a bridge between landscape architecture and social shifts, offering a multidisciplinary approach to comprehending human-nature linkages and supporting sustainable development.     

Correction to: 3D APT and NOE CEST-MRI of healthy volunteers and patients with non-enhancing glioma at 3 T

Magnetic Resonance Materials in Physics, Biology and Medicine -